It is known that when a car with wheels of radius 14 in. is driven at 35 mph, the wheels turn at an approximate rate of 420 revoulutions for minute. Show how to obtain this rate of turn.
If you ride a bicycle a distance of 5 miles in 15 minutes at a constant speed and if the bicycle's wheels have diameter 27 in., find the wheels approximate rate of turn (in revoultions per minute)
Can someone at least help me get started even if you cannot answer the question completely. Thanks
THe wheel has to cover 5 miles, right? So divide the 5miles by the wheel circumference to get the number of turns, and then divide by time.
Can you or someone else please clarify your explanation. Thank you.
What part of Mr. Pursley's explanation don't you understand? He's given you these steps:
Divide the 5 miles by the wheel circumference. That gives you the number of turns.
Divide the number of turns by the time.
I understand what he's telling me to do, but I've gone through it multiple times and it just doesn't seem correct.
What answer did you get?
If I understand the steps correctly, 27x 3.14= 84.78 divided by 5= 16.956 divided by 15= 1.1304 (which seems pretty slow) If you notice a mistake I have made in the procedure please let me know. Thanks
number of turns=5miles/(27inches*PI)
Now, you have to convert miles to inches to divide this out.
Then, after you get revolutions from the above, divide by 15 min to get rev/min
Thank you I appreciate all the help.
To find the approximate rate of wheel turn, we need to calculate the number of revolutions per minute (RPM). Here's how you can do it:
1. Start by converting the car's speed from miles per hour (mph) to inches per minute (in/min). Since there are 5,280 feet in a mile and 12 inches in a foot, you can use the following conversion:
Speed (in/min) = Speed (mph) * 5,280 ft/mile * 12 in/ft / 60 min
In this case, since the car is traveling at 35 mph, the calculated speed in in/min would be:
Speed (in/min) = 35 * 5,280 * 12 / 60 = 3,528 in/min
2. Next, determine the circumference of the car's wheels. The circumference of a circle can be calculated using the formula:
Circumference = 2 * π * Radius
In this case, the given radius is 14 inches, so the circumference would be:
Circumference = 2 * 3.14 * 14 = 87.92 inches
3. Now, divide the calculated speed by the circumference to obtain the number of revolutions per minute:
RPM = Speed (in/min) / Circumference
Plugging in the values, we get:
RPM = 3,528 / 87.92 ≈ 40.1 revolutions per minute
To solve the second question about the bicycle's wheels, we can follow the same steps:
1. Convert the distance traveled from miles to inches. Since there are 5,280 feet in a mile and 12 inches in a foot:
Distance (inches) = Distance (miles) * 5,280 ft/mile * 12 in/ft
In this case, the distance is 5 miles, so the calculated distance in inches would be:
Distance (inches) = 5 * 5,280 * 12 = 316,800 inches
2. Calculate the circumference of the bicycle's wheels using the given diameter, which is 27 inches:
Circumference = 2 * π * Radius
Radius = Diameter / 2 = 27 / 2 = 13.5 inches
Circumference = 2 * 3.14 * 13.5 = 84.78 inches
3. Divide the distance by the circumference to obtain the number of wheel revolutions:
Revolutions = Distance (inches) / Circumference
Plugging in the values, we get:
Revolutions = 316,800 / 84.78 ≈ 3,734 revolutions
4. Lastly, calculate the rate of turn in revolutions per minute. Since the bicycle took 15 minutes to cover the distance:
RPM = Revolutions / Time (minutes)
In this case, the time is 15 minutes, so the calculated rate of turn would be:
RPM = 3,734 / 15 ≈ 249 revolutions per minute